This is what a goat head thorn looks like.
We seem to have been running into these things all fall. They are definitely a nuisance. We have parked several places where they stick to shoes then come inside and come off on the floor to be stepped later with bare feet. Ouch! We have also pulled a number of them out of Roxie's feet. We have heard of them getting into a dog's feet and causing infections and vet bills. They even sell shoes for dogs to protect their feet.
They are very hard on bicycle tires. Dennis rides every day, often on places other than improved roads. As a result he has changed a number of tubes. He went into a bike shop in Hollister and bought a couple of heavy duty inner tubes. They also sell tire liners to go between the bottom of the tire and the inner tubes. We talked to someone in the campground who said that duct tape on the inside of the bicycle tire would work the same way (it just makes another layer that a thorn, piece of glass or other sharp object has to penetrate before it punctures the tube). So he tried it. So far, so good.